Dimensional Reduction in Quantum Gravity
Abstract
The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a twodimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why sofar no completely consistent mathematical models of quantum black holes have been found. Essay dedicated to Abdus Salam.
 Publication:

arXiv eprints
 Pub Date:
 October 1993
 arXiv:
 arXiv:grqc/9310026
 Bibcode:
 1993gr.qc....10026T
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 13 pages. TEX. 2 figures in postscript. Figures are now made visible if pdf file is downloaded